You will have to file nonresident tax returns in Arizona and Illinois, and a resident tax return in Virginia. The money you earned in AZ and IL is subject to tax by the state where you earned it. Since you are a resident of VA, all your income is subject to VA tax, no matter where you earned it.
The usual rule is that your resident state will give you credit for part or all of the tax that you pay to a nonresident state. However, VA and AZ have the opposite arrangement. AZ will give you credit for part or all of the tax that you pay to VA on your AZ income. To get the credits calculated correctly, I think you probably should prepare the state tax returns in this sequence: IL first, then VA, then AZ.
